Question

Find the APR, or stated rate, in each of the following cases: (Do not round intermediate calculations. Enter your answers as a percent rounded to 2 decimal places, e.g., 32.16.)

Stated Rate (APR)		Number of Times Compounded			Effective Rate (EAR)
	%		Semiannually		12.2	%
			Monthly		13.1
			Weekly		10.8
			Infinite		14.5

Answer 1

1.EAR=(1+APR/m)^m-1
where m=compounding periods

0.122=(1+APR/2)^2-1

(1+0.122)=(1+APR/2)^2

(1.122)^(1/2)=(1+APR/2)

APR=[(1.122)^(1/2)-1]*2

=11.85%(Approx).

2.EAR=(1+APR/m)^m-1
where m=compounding periods

0.131=(1+APR/2)^12-1

(1+0.131)=(1+APR/12)^12

(1.131)^(1/12)=(1+APR/12)

APR=[(1.131)^(1/12)-1]*12

=12.37%(Approx).

3.EAR=(1+APR/m)^m-1
where m=compounding periods

0.108=(1+APR/52)^52-1

(1+0.108)=(1+APR/52)^52

(1.108)^(1/52)=(1+APR/52)

APR=[(1.108)^(1/52)-1]*52

=10.27%(Approx).

4.EAR=(e)^APR-1
where e=2.71828

0.145=(2.71828)^APR-1

(1.145)=2.71828^APR

Taking log on both sides;

log 1.145=APR*log 2.71828

APR=log 1.145/log 2.71828

=13.54%(Approx).